Status of Tri/Bi-Maximal Neutrino Mixing

TL;DR

This paper reviews the status of tri/bi-maximal neutrino mixing, generalizes the ansatz, and explores the group-theoretic structure of the neutrino mass matrix in the context of S3 symmetry.

Contribution

It introduces a generalized TBM framework with S3 group structure and analyzes the quantum numbers characterizing neutrino states.

Findings

Neutrino mass matrix exhibits S3 group symmetry.

Neutrino states distinguished by mutativity and democracy quantum numbers.

Exact TBM corresponds to specific group-theoretic forms.

Abstract

Tri/bi-maximal mixing (TBM) is a specific lepton mixing ansatz, which describes the trend of the current neutrino oscillation data, in particular the recent SNO and KAMLAND results. The significant feature of TBM in this respect is |U_e2|^2=|U_m2|^2=|U_t2|^2=1/3, and we say that the nu_2 is tri-maximally mixed. We have generalised the TBM ansatz to a generic mixing matrix with the nu_2 trimaximally mixed, whereby the neutrino mass matrix in the lepton flavour basis takes the form of a general S3 group matrix (3 x 3 `magic-square'). In exact TBM the charged-lepton mass matrix in the neutrino mass basis (where the neutrino mass matrix is diagonal) takes the form of a general S3 class operator. The neutrino mass matrix in the flavour basis is a particular S3 group matrix which is also an S1 C S2 C S3 group-chain class operator, whereby the neutrino mass eigenstates are distinguished by their `mutativity' (M_i = +/-1) and `democracy' (D_i = 0,3) which are both good quantum numbers in exact TBM.